Rulings

Class cards have multiple text box sections. Other than the top section, each section contains a class level bar that includes a cost and a level number. Each represents an activated ability with the listed cost that advances the Class to the level listed in that bar.
An ability that advances a Class to a higher level is a normal activated ability. It uses the stack and can be responded to.
Each Class starts at level 1 and has the abilities in the top section of its text box. Once a Class advances to level 2 or level 3, it has all of the abilities listed in the associated section of its text box as well.
Leader's Talent's level 3 ability resolves before the spell that caused it to trigger. It resolves even if that spell is countered or otherwise leaves the stack.
You can't activate an ability that advances a Class to a particular level if that Class is already that level or higher. For example, if a Class is already level 2, you can't activate the ability that advances it to level 2 again.
Gaining a level won't remove abilities that a Class had at a previous level.
There's no restriction on how many Class permanents you can control, whether they're the same or different classes. Each Class permanent tracks its own level separately.